On the other hand...
If the extra cost is not a concern, and you go offshore for premed courses, do well in them and rock the MCAT, I don't think you'd be hurt, and you may be helped -- come on, it's premed, not clinical rotations where resources and quality of health care system will be reflective of your training. Sure, med schools look at where you get your undergrad degree, and some do care where you do your premed, but they also look for signs of maturity and independence and direction, and some will *like* that you took off somewhere to do your premed, e.g., "to experience another culture/system", etc. And it's the MCAT that's primarily used as the standard to compare abilities to absorb basic science across schools, not where you took the courses.
I'd guess that premed in Grenada is probably *better* than premed at 70-80% of US schools (and I hope, Renovar, you're not saying St. G's isn't "legit") -- there are a lot of crappy third-rate schools in the US, and many first-rate research schools with crappy lecturers (and research quality of a school adds zilch to intro (e.g., premed) science course quality). And doing premed somehere in the US that has a med school helps just slightly better than nil (spending a year doing med research directly with a PI is a different thing altogether).
So if what you want is a year or so of exotic or tropical living, go somewhere like Grenada, Ireland, Australia, even -- or maybe particularly -- Haiti. If the program sucks, then rely on yourself more and study harder, as premed can be 90% book-learned. Sure, you gotta' mix a few chemicals, maybe identify an unknown or two in lab, but you can do that anywhere with a chem set, and I personally thought the labs were a waste of time beyond getting comfortable with smart practices and protocols and expensive equipment...yippee, we prepared samples and pushed the button on the NMR, but the paper output is identical to what you'd find in a textbook. And while you're there studying 4-5 textbooks, learn something additional, other than premed, something that equates with personal development, that you can show to admin committees.
Just don't expect the premed course *grades* to help you much -- good grades are normally expected for premed courses, and probably a bit more so if there is any question by the admin committees on the program's quality. So, if you want to go somewhere to see somewhere else, and you're independent enough to thrive regardless of the program's quality, I say -- go for it.